The Influence of Isotopic Substitution on Band Position

If the bond strength in a diatomic molecule may be assumed to remain unchanged when an isotope is substituted for one of the atoms, the ratio of the frequencies of the band position before and after the substitution is given, as has been shown earlier, by the formula 

This formula can be used to calculate the approximate wave-number shift that occurs when an isotope is substituted in a diatomic molecule. It is only approximately correct for diatomic molecules. For other than diatomic molecules—where the masses of many atoms may be involved in a vibration, and where bending as well as stretching vibrations can occur—the use of this equation is even less satisfactory. 

The isotopic shift of a given vibrational frequency will be small if the atoms replaced by the isotopes participate only to a small extent in the vibration, but the shift will be large if these atoms play a major role. Thus, the shift an isotope produces can be used as a measure of the extent to which a particular atom participates in a vibration, provided no factors other than the change in mass are involved in the observed shift. A phenomenon such as Fermi resonance may be enhanced when an isotope is substituted into a molecule, if the shift brings frequencies more nearly into coincidence. 

We saw earlier that the frequency v sc at which a molecule would vibrate if it were a harmonic oscillator can be calculated from the observed position of the fundamental and overtone bands. If this frequency is first calculated for the normal molecule and then for 

For fairly symmetric polyatomic molecules it is possible to obtain an alternative expression for the frequency (or wavenumber) ratio between the normal and the isotopic molecule. For example, for the antisymmetric V3 frequencies of H2O and D2O this ratio is 

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